View source for Non self-consistent calculations: Band structures and Density Of States


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==Non self-consistent calculations: Intro==
[[File:Si band structure.png|right |thumb | Silicon band structure. Originals from [https://www.tf.uni-kiel.de/matwis/amat/td_kin_ii/index.html Thermodynamics and
Kinetics II, Dr. J. Carstensen, Univ. Kiel] ]]

Once the charge density has been obtained in a scf run, more calculations can be performed at fixed density (non-scf).
Among these:
* calculations of Kohn-Sham energies and orbitals on any given set of k-points (i.e. without specific aim of represent a reasonable sampling of the BZ);
* calculations as above, also increasing the number of computed (= diagonalized) bands (incl the calculation of empty Kohn-Sham states);
* Importantly, nscf calculations are typically done to plot KS bands or compute the DOS,
* but also as a preliminary step to other calculations (e.g. uniform k-point samplings and large amounts of empty states are using in GW and other many-body perturbation theory algorithms implemented with sum-over-states techniques)

In the Quantum ESPRESSO input file one has to set:

    calculation="nscf"    # kpts sampling BZ
or
    calculation="bands"   # kpts along lines

Some comments:
* <code>bands</code> is also a nscf-calculation strictly speaking (i.e. the charge density is clearly not updated).
* It differs from <code>calculation="nscf"</code> since there is not even the requirement of a uniform k-sampling (k-points can be computed along special directions, or just at any place in the BZ). 
* In this perspective, <code>nscf</code> runs can evaluate integrated quantities like an update of the Fermi energy.
* During nscf (as well as bands) KS eigenvalues are diagonal to full accuracy (<code>diago_full_acc=.true.</code> by default), at variance with scf calculations, where accuracy is lowered for empty states (not relevant to compute the density not the total energy).
* While one could set <code>diago_full_acc=.true.</code> in scf runs, it is anyway highly recommended to run a second nscf calculation to perform BZ refinements or increase the number of state for plotting or inspection.
* K-points (and number of bands if relevant) need to be specified according to the specific needs. See below for bands and DOS.


==DOS==

In this case a uniform k-point sampling is needed, similarly to scf calculations. 

A proper sampling of the BZ is then performed, but the density is not updated.

Input example (<code>pw.x</code> executable) to prepare for DOS calculations:
  [...]
  K_POINTS {automatic}
  20 20 20   0 0 0

By doing this we are de fact performing a refinement of the BZ sampling. 

Setting <code>calculation="nscf"</code> is a good choice.

Once the KS data have been produced by using <code>pw.x</code>, we can take advantage of a post-processing utility of QE,
<code>dos.x</code> to compute the actual DOS

  $>  dos.x < dos.in > dos.out

where a typical input file contains the following information:  
  $>  cat dos.in

  &DOS
      prefix = 'diamond'
      outdir = './SCRATCH/'
      
      degauss=0.01  !  [Ry]  broadening parameter
      
   [  Emin=val      !  min/max/step of the energy grid
      Emax=val
      deltaE=val
   ]
      fildos = 'dos_diamond.dat'
   /  

The output file can then be visualised using some standard tools as described in [[Plotting and visualization tools]].

==Band structure==

In this case we need to sample the BZ along user-defined segments in reciprocal space.

Such sampling can be either generated by the <code>pw.x</code>, see below, or provided explicitly by the user and <code>calculation="bands"</code> needs to be set. 

The conventions to define and label high symmetry k-points for different lattices can be found here: 
[https://www.materialscloud.org/work/tools/seekpath MaterialsCloud SeekPath]


Input example (<code>pw.x</code>) to produce the required KS data:

  [...]
  K_POINTS {crystal_b}
  6
  0.500  0.500  0.000   40    # X 
  0.000  0.000  0.000   40    # G 
  0.500  0.500  0.500   40    # L 
  0.750  0.500  0.250   40    # W 
  0.750  0.375  0.375   40    # K 
  0.000  0.000  0.000    1    # G 

Note that here 6 is the number of line edges (= 5 segments). 

Names of k-points are not required and just added to decorate the input file

Alternatively, one can provide the list of k-points explicitly.
The input file would look like:

  [...]
  K_POINTS {crystal}
  140
  0.500  0.500  0.000   1     # X
  0.490  0.490  0.000   1
  0.480  0.480  0.000   1
  [...]
  0.010  0.010  0.000   1
  0.000  0.000  0.000   1     # G 
  [...] 

* The first line provides the total number of input k-points.
* Each line contains the 3 components of the selected k-point (either in cartesian or crystal coords. 
* The extra column (filled with 1, here) is a placeholder for k-point weight (not used or <code>bands</code> runs)

Once the nscf data have been computed, <code>bands.x</code> (a post-processing utility of QE) can be used to cast the data in a form ready to be plotted.

  $ ./bands.x < bands.in > bands.out
where bands.in looks like:  
  &BANDS
     prefix = 'diamond'
     outdir = './SCRATCH/'
     filband = 'bands_diamond.dat'
  /   

As for <code>dos.x</code>, it is not difficult to parse the data directly from the output file of <code>pw.x</code> and reformat them by using your own tools.

An example of such a tool is provided in 
  LabQSM/tools/plot_bands.py

Note that in order to have all eigenvalues printed in the <code>pw.x</code> output file, you may need to set the variable
  &CONTROL
    [...]
    verbosity="high"
  /
(which can useful also in a number of other cases when you want extended info about the system studied).

==Examples and Exercises==


===Exercise1===
'''Band structure and DOS of Diamond'''

* Plot the DOS and the band structure of diamond along high-symmetry k-point lines
* Use the converged parameters and lattice constant obtained in previous calculations to run scf and nscf calculations

[[Solution_LAB1_bands_DOS_diamond | Solution]]


===Exercise2===
'''Band structure and DOS of Aluminium'''

* Plot the DOS and the band structure of Aluminium along high-symmetry k-point lines
* Al is a FCC crystal, 1 atom per cell, Exp lattice parameter: 4.0495 Ang
* '''Hint''': high symmetry kpts can be found in the Seek-path of materialscoulud: https://www.materialscloud.org/work/tools/seekpath

[[Solution_LAB1_bands_DOS_Aluminium | Solution]]


===Exercise3===
'''Band structure and DOS of GaAs'''

* Plot the DOS and the band structure of GaAs along high-symmetry k-point lines
* GaAs is a zinc-blende structure (fcc with 2 atoms per cell)
* '''Hint''': high symmetry kpts can be found in the Seek-path of materialscoulud: https://www.materialscloud.org/work/tools/seekpath

[[Solution_LAB1_bands_DOS_GaAs | Solution]]